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on Utility Models and Prospect Theory |
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Issue of 2024‒04‒15
twelve papers chosen by |
| By: | Nobuo Koida; Koji Shirai |
| Abstract: | This paper develops a novel characterization for random utility models (RUM), which turns out to be a dual representation of the characterization by Kitamura and Stoye (2018, ECMA). For a given family of budgets and its "patch" representation \'a la Kitamura and Stoye, we construct a matrix $\Xi$ of which each row vector indicates the structure of possible revealed preference relations in each subfamily of budgets. Then, it is shown that a stochastic demand system on the patches of budget lines, say $\pi$, is consistent with a RUM, if and only if $\Xi\pi \geq \mathbb{1}$. In addition to providing a concise closed form characterization, especially when $\pi$ is inconsistent with RUMs, the vector $\Xi\pi$ also contains information concerning (1) sub-families of budgets in which cyclical choices must occur with positive probabilities, and (2) the maximal possible weights on rational choice patterns in a population. The notion of Chv\'atal rank of polytopes and the duality theorem in linear programming play key roles to obtain these results. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.04328&r=upt |
| By: | NAKADA, Satoshi; SAKAMOTO, Norihito |
| Abstract: | This paper investigates a class of socialwelfare orderings that satisfy the standard and acceptable axioms in the literature: anonymity, strong Pareto, separability, and Pigou-Dalton transfer (or, convexity). Due to the lack of continuity, we show that the class of social welfare orderings typically has some thresholds satisfying the following property, which we call level-oligarchy: individuals whose utility is less than the value are prioritized over the other individuals whose utility is greater than the value. First, we provide the novel reduced form characterization that a social welfare ordering satisfies anonymity, strong Pareto, separability, and convexity must be either the weak generalized utilitarian or level-oligarchy. Next, by dropping convexity and instead requiring Pigou-Dalton transfer and a mild continuity axiom, we characterize the new class of social welfare orderings, the multi-threshold generalized sufficientarian orderings, which subsumes the leximin, generalized utilitarian, and critical-level sufficientarian social welfare orderings as special cases. Therefore, we can provide a unified characterization for the important class of social welfare orderings only by the permissible axioms. In particular, although the social judgment from both classes of orderings seems quite different, our result implies that the difference between the utilitarian and leximin orderings just comes from the degree of continuity. |
| Keywords: | Social welfare ordering, utilitarian, leximin, sufficientarianism, distributive justice |
| JEL: | D31 D63 D70 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:hit:rcnedp:13&r=upt |
| By: | Alexis Direr (LEO - Laboratoire d'Économie d'Orleans [2022-...] - UO - Université d'Orléans - UT - Université de Tours - UCA - Université Clermont Auvergne) |
| Abstract: | I study the allocation problem of investors who hold their portfolio until reaching a target wealth. The strategy suppresses final wealth uncertainty but creates a time horizon risk. I begin with a classical mean variance model transposed in the duration domain, then study a dynamic portfolio choice problem with Generalized Expected Discounted Utility preferences. Using long-term US return data, I show in the mean variance model that a large amount of time horizon risk can be diversified away by investing a significant share of equities. In the dynamic model, more impatient investors are also more averse to timing risk and invest less in equities. The optimal equity share is downward trending as accumulated wealth approaches its target. |
| Keywords: | timing risk, portfolio choice, risk aversion |
| Date: | 2023–12–29 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04501750&r=upt |
| By: | Valerio Capraro; Roberto Di Paolo; Matjaz Perc; Veronica Pizziol |
| Abstract: | Understanding human behaviour in decision problems and strategic interactions has wide-ranging applications in economics, psychology, and artificial intelligence. Game theory offers a robust foundation for this understanding, based on the idea that individuals aim to maximize a utility function. However, the exact factors influencing strategy choices remain elusive. While traditional models try to explain human behaviour as a function of the outcomes of available actions, recent experimental research reveals that linguistic content significantly impacts decision-making, thus prompting a paradigm shift from outcome-based to language-based utility functions. This shift is more urgent than ever, given the advancement of generative AI, which has the potential to support humans in making critical decisions through language-based interactions. We propose sentiment analysis as a fundamental tool for this shift and take an initial step by analyzing 61 experimental instructions from the dictator game, an economic game capturing the balance between self-interest and the interest of others, which is at the core of many social interactions. Our meta-analysis shows that sentiment analysis can explain human behaviour beyond economic outcomes. We discuss future research directions. We hope this work sets the stage for a novel game theoretical approach that emphasizes the importance of language in human decisions. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.08944&r=upt |
| By: | Bramoullé, Y.; Ghiglino, C. |
| Abstract: | We introduce loss aversion into a model of conspicuous consumption in networks. Agents allocate heterogeneous incomes between a conventional good and a status good. They interact over a connected network and compare their status consumption to their neighbors’ average consumption. We find that aversion to lying below the social reference point has a profound impact. If loss aversion is large relative to income heterogeneity, a continuum of conformist Nash equilibria emerges. Agents have the same status consumption, despite differences in incomes and network positions, and the equilibrium is indeterminate. Otherwise, there is a unique Nash equilibrium and status consumption depends on the interplay between network positions and incomes. Our analysis extends to homothetic and heterogeneous preferences. |
| Keywords: | Conspicuous Consumption, Loss Aversion, Social Networks |
| Date: | 2024–03–12 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camjip:2409&r=upt |
| By: | Tomohito Aoyama; Nobuyuki Hanaki |
| Abstract: | The random incentive system (RIS) is a standard incentive scheme used to elicit preferences in economic experiments. However, it has been speculated that RIS may not be incentive compatible when participants are concerned about ambiguity, i.e., that the choices observed under RIS do not reflect the underlying preferences. To examine the performance of RIS under ambiguity, we conducted three experiments online and in a laboratory. The results of the experiments suggest that RIS is incentive compatible. We argue that presenting choice situations in isolation may improve the incentive compatibility of RIS. We also argue that using RIS, together with an experimental guideline called Prince, may reduce the observed ambiguity aversion. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1236&r=upt |
| By: | Takuma Kunieda (Kwansei Gakuin University); Akihisa Shibata (Kyoto University) |
| Abstract: | Although many studies in macroeconomics have examined the role of insurance in the presence of income risk, whether aggregate shocks are insurable has not been sufficiently investigated. We present a simple two-period general equilibrium model to show the conditions under which insurance against aggregate shocks works in an economy with constant-elasticity-substitution (CES) production technology and the Greenwood- Hercowitz-Huffman (GHH) utility function (Greenwood et al., 1988). Our theoretical investigation clarifies that only when agents are heterogeneous in their ability or initial wealth can aggregate shocks be insurable. From our quantitative investigation, we find that (i) agents with lower ability enjoy greater welfare improvement from insurance, and as agents’ ability increases, the welfare improvement diminishes, (ii) agents enjoy greater welfare improvement when the damage from disasters is more severe and when the frequency of disasters is greater, and (iii) although the welfare improvement increases as agents’initial wealth increases, the impact of a difference in agents' initial wealth on the difference in the contribution of insurance is very moderate. |
| Keywords: | aggregate shocks, heterogeneous agents, state-contingent claims, incomplete market |
| JEL: | D52 G12 |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:1102&r=upt |
| By: | Ichiro Muto (General Manager, Aomori Branch, Bank of Japan (E-mail: ichirou.mutou@boj.or.jp)); Fumitaka Nakamura (Director, Institute for Monetary and Economic Studies, Bank of Japan (currently, International Monetary Fund, E-mail: fumitaka.nakamura@boj.or.jp)); Makoto Nirei (Professor, Graduate School of Economics, University of Tokyo (E-mail: nirei@e.u-tokyo.ac.jp)) |
| Abstract: | What are the main drivers of the recent increase in wealth concentration in the U.S.? This paper quantifies the role played by digitalization using a tractable model with heterogeneous agents with risk aversion. The model combines (1) digital capital that substitutes for labor in the production process and (2) households' investments in risky digital assets to replicate the asset growth of the wealthy since the 1990s. In the equilibrium, a small number of prosperous households with low risk aversion, i.e., digital entrepreneurs, hold most of the risky digital capital, whereas a large number of risk-averse households rely mainly on labor income. Hence, when digitalization advances, these risk-tolerant households enjoy higher returns from digital capital, further accumulating digital capital disproportionately. Based on the model calibrated to the U.S. economy, we show that digitalization (an increase in digital productivity by 21-43 percent) has contributed to more than about 50 percent of the increase in the share of wealth of the top 1 percent of households and more than about 80 percent of that of the top 0.1 percent of households observed over the last 30 years. Moreover, it explains about 20-40 percent increase in the annual savings of the top 1 percent of households. Finally, the comparative statics on the macroeconomic variables show that while advances in digitalization decrease the labor share by 3-5 percentage points, which is in line with the empirical literature, it also increases wages, meaning that risk- averse households, who rely mainly on labor earnings, also gain some benefits from digitalization. |
| Keywords: | Digitalization, Entrepreneurship, Wealth inequality, Savings inequality |
| JEL: | E21 E22 E24 E25 |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:24-e-01&r=upt |
| By: | Xin Yue Ren; Dena Firoozi |
| Abstract: | In this paper, we address linear-quadratic-Gaussian (LQG) risk-sensitive mean field games (MFGs) with common noise. In this framework agents are exposed to a common noise and aim to minimize an exponential cost functional that reflects their risk sensitivity. We leverage the convex analysis method to derive the optimal strategies of agents in the limit as the number of agents goes to infinity. These strategies yield a Nash equilibrium for the limiting model. The model is then applied to interbank markets, focusing on optimizing lending and borrowing activities to assess systemic and individual bank risks when reserves drop below a critical threshold. We employ Fokker-Planck equations and the first hitting time method to formulate the overall probability of a bank or market default. We observe that the risk-averse behavior of agents reduces the probability of individual defaults and systemic risk, enhancing the resilience of the financial system. Adopting a similar approach based on stochastic Fokker-Planck equations, we further expand our analysis to investigate the conditional probabilities of individual default under specific trajectories of the common market shock. |
| Date: | 2024–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2403.03915&r=upt |
| By: | Selim Mankaï (IAE - UCA - Institut d'Administration des Entreprises - Clermont-Auvergne - UCA - Université Clermont Auvergne, UCA - Université Clermont Auvergne); Sébastien Marchand (CERDI - Centre d'Études et de Recherches sur le Développement International - IRD - Institut de Recherche pour le Développement - CNRS - Centre National de la Recherche Scientifique - UCA - Université Clermont Auvergne, UCA - Université Clermont Auvergne); Ngoc Ha Le (UCA - Université Clermont Auvergne) |
| Abstract: | The demand for voluntary insurance against low-probability, high-impact risks is lower than expected. To assess the magnitude of the demand, we conduct a meta-analysis of contingent valuation studies using a dataset of experimentally elicited and survey-based estimates. We find that the average stated willingness to pay (WTP) for insurance is 87% of expected losses. We perform a meta-regression analysis to examine the heterogeneity in aggregate WTP across these studies. The meta-regression reveals that information about loss probability and probability levels positively influence relative willingness to pay, whereas respondents' average income and age have a negative effect. Moreover, we identify cultural sub-factors, such as power distance and uncertainty avoidance, that provided additional explanations for differences in WTP across international samples. Methodological factors related to the sampling and data collection process significantly influence the stated WTP. Our results, robust to model specification and publication bias, are relevant to current debates on stated preferences for low-probability risks management. |
| Abstract: | La demande d'assurance volontaire contre les risques à faible probabilité et à fort impact est plus faible que prévu. Pour l'ampleur de la demande, nous effectuons une méta-analyse des études d'évaluation contingente à l'aide d'un d'estimations obtenues expérimentalement et basées sur des enquêtes. Nous constatons que le consentement à payer (CAP) moyen déclaré à payer (CAP) pour l'assurance est de 87 % des pertes attendues. Nous effectuons une analyse de méta-régression pour examiner l'hétérogénéité de la volonté de payer globale dans ces études. La méta-régression révèle que les informations sur la probabilité des pertes et les niveaux de probabilité influencent positivement la volonté relative de payer, tandis que le revenu moyen et l'âge des personnes interrogées ont un effet positif sur la volonté de payer. le revenu moyen et l'âge des répondants ont un effet négatif. En outre, nous identifions des sous-facteurs culturels, tels que la distance de pouvoir et l'évitement de l'incertitude, qui ont fourni des explications supplémentaires pour les différences de consentement à payer entre les échantillons internationaux. de la volonté de payer dans les échantillons internationaux. Les facteurs méthodologiques liés à l'échantillonnage et à la collecte des données d'échantillonnage et de collecte des données influencent de manière significative le CAP déclaré. Nos résultats, robustes à la spécification du modèle et au biais de publication, sont pertinents pour les débats actuels sur l'acceptation de paiement. de publication, sont pertinents pour les débats actuels sur les préférences déclarées en matière de gestion des risques à faible probabilité. |
| Keywords: | Low probability risks, Contingent valuation, Insurance demand, Stated preferences method, Metaanalysis, Economic experiments |
| Date: | 2024–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04474880&r=upt |
| By: | SAKAMOTO, Norihito |
| Abstract: | This paper revisits impossibility results on the tyrannies of aggregation and non-aggregation. I propose two aggregation principles --quantitative aggregation and ratio aggregation—and investigate theoretical implications. As a result, I show that quantitative aggregation and minimal non-aggregation are incompatible while ratio aggregation and minimal non-aggregation are compatible under the assumption of standard axioms in social choice theory. Furthermore, this study provides a new characterization of the leximin rule by using replication invariance and the strong version of non-aggregation. Finally, I propose a class of practical and acceptable social welfare orderings that satisfy the principles of aggregation and non-aggregation, which has various advantages over the standard rank-discounted generalized utilitarianism. |
| Date: | 2024–02 |
| URL: | http://d.repec.org/n?u=RePEc:hit:rcnedp:12&r=upt |
| By: | Giebe, Thomas (Department of Economics and Statistics); Gürtler, Oliver (Department of Economics, University of Cologne) |
| Abstract: | In competitive settings, disparities in player strength are common. It is intuitively unclear whether a stronger player would opt for larger or smaller effort compared to weaker players. Larger effort could leverage their strength, while lower effort might be justified by their higher probability of winning regardless of effort. We analyze contests with three or more players, exploring when stronger players exert larger or lower effort. To rank efforts, it suffices to compare marginal utilities in situations where efforts are equal. Effort ranking depends on differences in hazard rates (which are smaller for stronger players) and reversed hazard rates (which are larger for stronger players). Compared to weaker players, stronger players choose larger effort in winner-takes-all contests and lower effort in loser-gets-nothing contests. Effort rankings can be non-monotonic in contests with several identical prizes, and they depend on the slopes of players’ pdfs in contests with linear prize structure. |
| Keywords: | contest theory; heterogeneity; player strength |
| JEL: | C72 D74 D81 |
| Date: | 2024–03–06 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:vxesta:2024_004&r=upt |